An approximate analytical scheme is presented to estimate landfill methane emissions taking into account the oxidation that occurs in the soil cover. To facilitate the solution of the methane transport equation we introduce a region dependent coefficient to account for the methane oxidation. Expressions for the distribution of methane concentration and methane flux inside the landfill and cover regions are obtained. The approach was applied to the CTVA-Caieiras landfill which was modeled as a vertical one-dimensional landfill with homogenous solid waste and soil cover regions. The methane emission obtained for the landfill was 2x10^-5 mol m^-2s^-1 for a 4 year old deposited waste with a 0.5 m soil cover. The calculation compared well with the median of 11 field measurements conducted at the CTVA-Caieiras. The emission rates were strongly dependent on the oxidation coefficient utilized, which varies with the cover material and microclimate conditions of the site. The oxidation coefficient can be interpreted as the probability per unit of time of methane oxidation in the medium. The scheme provides a qualitative description of the methane transport and oxidation phenomena in landfills.